Dynamic Sculpting and Deformation
of Point Set Surfaces
Xiaohu Guo Hong Qin
Department of Computer Science
SUNY Stony Brook
Outline
Introduction and motivation
Dynamic point set surfaces
Local surface distance field via scalar trivariate B-splines
Global surface distance field via Shepard’s blending
Dynamic volumetric model
Editing toolkits & Results
Conclusions and future work
Outline
Introduction and motivation
Dynamic point set surfaces
Local surface distance field via scalar trivariate B-splines
Global surface distance field via Shepard’s blending
Dynamic volumetric model
Editing toolkits & Results
Conclusions and future work
Introduction and motivation
Point sampled geometry is ubiquitous
Acquisition Modeling Rendering
• laser scanning • deforming • surface splatting
• image scanning • sculpting • Qsplat
• etc. • cutting/pasting • hardware acc.
• painting • etc.
• etc.
Interactive shape control
Dynamic behavior of objects
User interactivity
Introduction and motivation
Implicit Modeling
Arbitrary topology, complicated geometry
Powerful physics-based modeling
Point based
geometry + Implicit modeling
Introduction and motivation
Our point geometry Local implicit distance field
representation
Shepard’s blending
Unstructured point
samples
Global implicit distance field
Local and Global implicit
distance field
Dynamic implicit
volumetric model Implicit volumetric model
Boolean Interactive Level set editing,
operation sculpting Global FFD……
Introduction and motivation
Previous work on point based geometry:
Surface reconstruction from unorganized points. H. Hoppe, et al. 1992.
The approximation power of moving least squares. D. Levin. 1998.
Point Set Surfaces. M. Alexa, et al. 2001.
Efficient simplification of point-sampled surfaces. M. Pauly, et al. 2002.
Shape modeling with point-sampled geometry. M. Pauly, et al. 2003.
QSplat: A multiresolution point rendering system for large meshes. S.
Rusinkiewicz, M. Levoy. 2000.
Surface splatting. M. Zwicker, et al. 2001.
Pointshop3D: An interactive system for point-based surface editing. M.
Zwicker, et al. 2002.
etc.
Introduction and motivation
Previous work on implicit modeling
Interactive techniques for implicit modeling. J. Bloomenthal, B.Wyvill.
1990.
Three dimensional freeform sculpting via zero sets of scalar trivariate
functions. A. Raviv and G. Elber. 1999.
Haptics-based volumetric modeling using dynamic spline-based implicit
functions. J. Hua, H. Qin. 2002.
Multi-level Partition of Unity Implicits. Y. Ohtake, A. Belyaev, M. Alexa,
G. Turk, H. Seidel. 2003.
etc.
Outline
Introduction
Dynamic point set surfaces
Local surface distance field via scalar trivariate B-splines
Global surface distance field via Shepard’s blending
Dynamic volumetric model
Editing toolkits & Results
Conclusions and future work
Dynamic point set surface
Local surface distance field
Unstructured point cloud:
P = { pi | 1 ≤ i ≤ N}
Fitting a volumetric implicit function to
the local distance field of each point
(Scalar trivariate B-spline function) :
l −1 m −1 n −1
s (u , v , w ) = ∑∑∑P ijk B i ,r (u )C j ,s ( v ) D k ,t ( w )
i=0 j=0 k =0
Minimizing the weighted least squares error:
k
∑ (s(u j , v j , w j ) − d j ) 2 θ ( p j − pi )
j =1
Dynamic point set surface
Fast reconstruction of local distance field:
Sample the trivariate function at a fixed
local grids:
(u1 , v1 , w1 )
G = {(u i , v i , wi ) | i ∈ [0, g ]}
The trivariate function can be simplified as
the matrix form:
s = (B ⊗ C ⊗ D)p
Easily reconstruct the trivariate function by:
(u 9 , v 9 , w9 )
[ ]
-1
p = (B ⊗ C ⊗ D) (B ⊗ C ⊗ D) (B ⊗ C ⊗ D) T d
T
Dynamic point set surface
Global distance field
Shepard’s blending:
N
∑ s ( x, y, z )φ ( x, y, z )
i =1
i i
s ( x, y , z ) = N
∑ φ ( x, y , z )
i =1
i
Dynamic point set surface
Dynamic volumetric model
Global region of interest
Resample the distance value at the
voxel grids
Deformation of the global scalar field
Deformation of the point set surface
Dynamic point set surface
Deformation of global scalar field
force force
Dynamic point set surface
Deformation of global scalar field
Lagrangian dynamics:
d is the vector of scalar values on the mass voxel grids.
Local editing: construct and deform the global
scalar field only on the surface of interest.
Please refer to:
Haptics-based volumetric modeling using dynamic
spline-based implicit functions. J. Hua and H. Qin.
IEEE/ACM SIGGRAPH Symposium on Volume
Visualization and Graphics 2002.
Dynamic point set surface
Dynamic updating of local domains
The trajectory of the point samples:
{x(t ) | s(x(t ), p(t )) = 0}
The derivative of s with respect to time yields:
ds ( x(t ), p(t )) ∂s ( x(t ), p(t )) dx ∂s ( x(t ), p (t )) dp
= + =0
dt ∂x dt ∂p dt
The speed of the point along its normal direction is:
Dynamic point set surface
Dynamic sampling
Up-sampling: Voronoi vertex method
in [M. Alexa, et al. 2001]
Down-sampling: Iterative method in
[M. Pauly, et al. 2002], not yet
implemented in our system.
Outline
Introduction
Dynamic point set surfaces
Local surface distance field via scalar trivariate B-splines
Global surface distance field via Shepard’s blending
Dynamic volumetric model
Editing toolkits & Results
Conclusions and future work
Editing toolkits
Geometric/topological tools
Embossing/engraving
Boolean operation
Force-based tools
Sculpting
Direct point-based rendering for all examples!
Editing toolkits
Embossing/engraving
Editing toolkits
Boolean operations
Sharp Intersections: represented as 2 different implicit surfaces
Editing toolkits
Force-based tools
Point-force tool & Curve-force tool
Experimental results
Local sculpting: 5 ~10 frames/second
Experimental results
Experimental results
Conclusions
Unstructured point samples as the modeling and
rendering primitives.
Scalar trivariate B-splines + Shepard’s blending
method for local and global distance fields.
A unified framework integrating point set
geometry with implicit modeling.
A dynamic sculpting and deformation scheme of
the point set surfaces.
Local editing on the point set surfaces.
Our approach can be readily integrated with
haptics interface.
Future work
Global deformation
Scalar field free-form deformation
Level set editing
Other manipulating toolkits
All of the above are based on point-
sampled geometry!
Acknowledgements
NSF grants IIS-0082035 and IIS-0097646
Alfred P. Sloan Fellowship
Colleagues from the Center of Visual
Computing, SUNY Stony Brook.
Thank you!